Final answer:
The buyer can make 1,287 possible selections of four Persian rugs and four Chinese rugs.
Step-by-step explanation:
The buyer can select four Persian rugs and four Chinese rugs from a group of Persian rugs and nine Chinese rugs. Since the buyer is selecting both Persian and Chinese rugs, this is an example of a combination problem. The number of possible selections can be calculated using the combination formula, which is given by:
C(n, r) = n! / ((n - r)! * r!)
Where n is the total number of options and r is the number of options to be selected.
In this case, there are 4 Persian rugs and 9 Chinese rugs, so n = 4 + 9 = 13. The buyer wants to select 4 Persian rugs and 4 Chinese rugs, so r = 4 + 4 = 8.
Plugging these values into the combination formula, we get:
C(13, 8) = 13! / ((13 - 8)! * 8!) = (13! / 5! * 8!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 154,440 / 120 = 1,287
So, there are 1,287 possible selections that the buyer can make.